UV Map not being applied to object
To set up textures properly follow these steps:

Cycles Render 

1. Select the material and open Node Editor window
2. Add an Image Texture node, then load the texture and connect Color to Diffuse BSDF node.
3. Add a UV Map node and select proper UV Map if you have more than one on the mesh and connect the node to the Vector of Image Texture node



Blender Render

1. Open materials tab.
2. Create a material or if there is one already existing, make sure the material you want to add the texture to is selected.



3. While the material is selected open texture tab.
4. In texture tab scroll down to Image section and open the texture you want to apply to the material.
5. In mapping section make sure the Coordinates are set to UV and choose the correct UV map in case you have more than one on the mesh.